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Mathematical Vignettes is a collection of short introductions (vignettes) about assorted topics in mathematics and related fields such as cryptography. Some of the topics are considered to be pure mathematics (e.g., number theory, Diophantine equations and continued fractions) while other topics fit into the realm of applied mathematics (e.g., stochastic processes, linear programming and cryptography). An effort has been made to keep the necessary background for reading each section to a minimum. Prerequisite knowledge is listed for each section (in some cases, pointing to sections within the book). There are many references for further study. References to free sources have been used as much as possible, e.g., Wikipedia, free online articles, YouTube videos and books that are available for electronic borrowing from the Internet Archive. There are also many references to online tools where the reader can experiment with the concepts being explained. Proofs of theorems are included in cases where the proofs are constructive (i.e., the proof entails an algorithm or method of solution) or where the proof adds further understanding of the topic